Closing the Gap: The Quest to Understand Prime Numbers narrates progress on the Twin Prime Conjecture made from the breakthrough work of Dr. Yitang Zhang in May 2013 (proving the existence of infinitely many pairs of twin primes that are at most 70 million apart) through the incremental “closing of the gap” achieved through the collaborative Polymath project.
It’s a challenging task to write about non-elementary topics in pure mathematics for a popular audience. Vicky Neale’s Closing the Gap is widely regarded as an exemplar in accomplishing this for the Twin Prime Conjecture. Neale artfully explains the essence of the Twin Prime Conjecture as well as related mathematical conjectures and theorems whose proofs have supported or may support its ultimate resolution. She captures through the book’s sixteen chapters not only the difficult mathematics undertaken to confront the conjecture, but also the nature of mathematics research today.
For the first gathering of the AWM Book Club in B-Term, with Closing the Gap as a basis, we discussed:
- The standing “record” for the smallest gap proven
- How close current methods can bring the gap to 2
- Whether we believe that the Twin Primes Conjecture is true
- The nature of the Polymath Project for this problem